The aforementioned patent and patent application disclose and claim a pumping system in which a quantity of pressurized product is stored in a storage compartment during a pressurizing stroke and discharged through an outlet orifice during a succeeding intake stroke to maintain a stream or spray issuing from the system. The patent application is particularly concerned with a trigger pump which is desirable for some applications, particularly where high pressure is desired. There are other applications in which a button actuated pump is more desirable, but button actuated pumps are typically low pressure pumps. The present invention is directed to providing a high pressure button actuated pumping system, and particularly such a high pressure pumping system which can be primed at low pressure.